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<p>In this paper the Bernstein-Doetsch generalize to the setting of strongly <i>n</i>-Jensen convexity. We also prove that the strongly <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {K}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">K</mi> </math></EquationSource> </InlineEquation>-convex function (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbb {K}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">K</mi> </math></EquationSource> </InlineEquation> is a subfield of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathbb {R}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">R</mi> </math></EquationSource> </InlineEquation>) admit a continuous strongly <i>n</i>-convex function.</p>

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On the Strongly Convexity of High Order

  • 期刊论文

  • 发表日期：

    2026年3月26日

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  • Mahmood Kamil Shihab

摘要

In this paper the Bernstein-Doetsch generalize to the setting of strongly n-Jensen convexity. We also prove that the strongly \(\mathbb {K}\) K -convex function ( \(\mathbb {K}\) K is a subfield of \(\mathbb {R}\) R ) admit a continuous strongly n-convex function.